LABORATORY COMPACTION CHARACTERISTICS AND MOISTURE-

DENSITY RELATIONSHIP OF SUBGRADE, EMBANKMENT SOILS, AND TXDOT DESIGNATION: TEX-114-E

BACKFILL MATERIAL

Test Procedure for

LABORATORY COMPACTION CHARACTERISTICS

AND MOISTURE-DENSITY RELATIONSHIP OF Texas
Department

SUBGRADE, EMBANKMENT SOILS, AND BACKFILL

of Transportation

MATERIAL

TxDOT Designation: Tex-114-E

Effective Dates: February 2005–January 2011.

1. SCOPE

1.1 Use this test method to determine the relationship between water content and the dry unit
mass (density) of sub-grade and embankment materials.

1.1.1 Part I is a subgrade or embankment sample, 4 in. (101.6 mm) in diameter and 6 in.
(152.4 mm) high, is molded in four layers, using a 5.5-lb. (2.5-kg) hammer dropped 25
times per layer from a height of 12 in. (304.8 mm). This part is intended for plastic and
fine-grain soils, such as silts and clays (ML, MH, CL, and CH classifications as
determined by Tex-142-E.)

1.1.2 Part II is a subgrade or embankment sample, 6 in. (152.4 mm) in diameter and 8 in.
(203.2 mm) high, is molded in four layers using a 5.5-lb. (2.5-kg) hammer dropped
75 times per layer from a height of 12 in. (304.8 mm). This part is intended for plastic,
and coarse-grain soils, such as sands and gravels with fines (GM, GC, SM, and SC
classifications as determined by Tex-142-E.)

1.1.3 Part III is a cohesionless backfill (sand/silt) sample, 4 in. (101.6 mm) in diameter and
6 in. (152.4 mm) in height, is molded in four layers, using a 10-lb. (4.54-kg) hammer
dropped 61 times per layer from a height of 12 in. (304.8 mm). Perform the test in Part III
on prepared materials passing the 1/4-in. (6.3-mm) sieve. This part is intended for clean,
cohesionless sands used for MSE backfill (SW and SP classifications as determined by
Tex-142-E.)

1.2 Follow Tex-113-E to determine moisture-density relationships of base materials, coarse-

grained materials containing particles larger than 7/8 in. (22.4 mm), and treated subgrade
and embankment materials.

1.3 The values given in parentheses (if provided) are not standard and may not be exact
mathematical conversions. Use each system of units separately. Combining values from
the two systems may result in nonconformance with the standard.

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DENSITY RELATIONSHIP OF SUBGRADE, EMBANKMENT SOILS, AND TXDOT DESIGNATION: TEX-114-E
BACKFILL MATERIAL

2. DEFINITIONS

2.1 Maximum Dry Density (Da)—Maximum dry density is the maximum value obtained by
the compaction curve using the specified compactive effort.

2.2 Optimum Water Content (Wopt)—Optimum water content is the water content at which
the soil can be compacted to the Da.

2.3 Compactive Effort (C.E.)—Compactive effort is the total energy, expressed as foot-
pounds per cubic inch (kilo-Newton-meters per cubic meter) used to compact the
specimen.
 C.E. is calculated as follows:

Ht. of Drop ( ft or m) × Wt. of Hammer (kN or lb) × # Drops × # Layers

Volume of Mold (m 3 or in 3 )
 This procedure requires, for Part I and Part II, 7.30 ft.-lb./in.3 (604 KN-m/m3) and,
for Part III, 32.36 ft.-lb./in.3 (2677 kN-m/m3), equivalent to ASTM "D 1557.

3. APPARATUS

3.1 Automatic tamper (compaction) device, with:

 Base plate to hold 4 in. (101.6 mm) or 6 in. (152.4 mm) inside diameter (ID)
forming molds
 5.5 lb. ±0.02 lb. (2.5 kg ±0.01 kg) sector-face rammer
 10 ±0.02 lb. (4.55 ±0.01 kg) sector-face rammer
 Adjustable drop height
 Striking face of the rammer conforming to a 43 ±2° segment of a 2.9 ±0.1 in.
(74±2.5 mm) radius circle
 Rigid foundation, such as a concrete block with a mass of not less than 200 lb.
(91 kg) on which the base plate of the tamper is secured. (An alternate foundation
support, such as a rigid stand or table, is allowed if the Da produced is within 2%
of that produced by an automatic tamper bolted to a concrete floor).

3.2 Rigid metal compaction mold, with 4 ±1/64 in. (101.6 ±0.4 mm) average ID and a height
of 6 ±0.0026 in. (152.4 ±0.7 mm) with removable collar, and/or a 6 in., +1/16 or -1/64 in.
(152.6 mm, +1.6 or -0.4 mm) average ID and a height of 8-1/2 ±1/16 in. (215.9 ±1.6 mm)
with removable collar.

3.3 Metal stand, with a set of standard spacer blocks and a micrometer dial assembly, with
2 in. (50 mm) travel, for determining height of specimens. Spacer blocks 1, 4, 6, and
11 in. (25.4, 101.6, 152.4, and 279.4 mm) accurate to 0.001 in. (0.025 mm).

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DENSITY RELATIONSHIP OF SUBGRADE, EMBANKMENT SOILS, AND TXDOT DESIGNATION: TEX-114-E
BACKFILL MATERIAL

3.4 Balance, with a minimum capacity of 35 lb. (15 kg), accurate and readable to 0.001 lb.
(0.5 g) or 0.1% of the test mass, whichever is greater.

3.5 Extra base plate, secured on a rigid stand to hold the forming mold.

3.6 Hydraulic press, to extrude molded specimens.

3.7 Drying oven, maintained at 230 ±9°F (110 ±5°C).

3.8 Metal pans, wide and shallow for mixing and drying materials.

3.9 Circular porous stones, slightly less than 6 in. (152.4 mm) in diameter and 2 in. (51 mm)
high.

3.10 Supply of small tools, including a 4 to 5-lb. (1.8 to 2.3-kg) rawhide hammer, level,
finishing tool, and others.

3.11 Standard U.S. sieves, meeting the requirements of Tex-907-K, in the following sizes:
 1-3/4 in. (45 mm)
 7/8 in. (22.4 mm)
 3/8 in. (9.5 mm)
 No. 4 (4.75 mm).

4. CALIBRATING EQUIPMENT

4.1 Calibrate equipment in accordance with Tex-198-E. In addition, calibrate equipment

before initial use, after repair, or after any occurrence that might affect the test results.

4.2 Follow the steps outlined in Tex-113-E, Section 4.

PART I—MEASURING MOISTURE-DENSITY RELATIONSHIP OF

SUBGRADE AND EMBANKMENT SOILS

5. SCOPE

5.1 Part I uses a 4-in. (102 mm) ID mold and applies only to soils with:
 100% passing the 3/8 in. (9.5 mm) sieve
 ≥ 80% passing the 1/4 in. (6.3 mm) sieve
 ML, MH, CL, and CH soil classification as determined by Tex-142-E.

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DENSITY RELATIONSHIP OF SUBGRADE, EMBANKMENT SOILS, AND TXDOT DESIGNATION: TEX-114-E
BACKFILL MATERIAL

6. PREPARING SAMPLE

6.1 Prepare the material in accordance with Tex-101-E, Part II. Do not use materials that
have been previously laboratory compacted.

7. PROCEDURE

7.1 Determine the percent hygroscopic moisture of a representative sample of prepared

material in accordance with Tex-103-E.

7.2 Separate sample on 7/8 in. (22.4 mm), 3/8 in. (9.5 mm), and 1/4 in. (6.3 mm) sieves and
determine particle size distribution.

7.3 Estimate the mass of air-dried material that will fill the mold when wetted and
compacted.

7.4 Using this estimated mass, and the percentages of the various sizes of particles obtained
in Section 7.2, compute the cumulative masses of each size to combine to make a
specimen.

7.5 Using the masses calculated in Section 7.3, recombine at least four specimens of
approximately 7.7 lb. (3.5 kg) each.

7.6 Estimate the optimum percent moisture required to attain maximum density.
Note 1—The plastic limit is a good indicator of optimum moisture content, typically
within 2%, or 3-4% higher for PI >35 material.

7.7 Start the M-D curve using a sample with a moisture content of 2% below the estimated
optimum moisture content. For soils with a low to moderate plasticity index (PI < 35),
adjust the moisture content of the remaining samples in approximately 2% increments to
attain 2 samples above and 2 samples below the optimum moisture content. For soils with
high plasticity index (PI ≥ 35), the moisture content may be adjusted in 4% increments to
attain two samples above and two samples below the optimum moisture.
Note 2—After compacting the first two or three specimens, construct the initial M-D
curve to aid in evaluation of the shape of the curve. If necessary, adjust the water content
of the other prepared samples by adding additional water or air-drying to obtain a well-
defined compaction curve.

7.8 Calculate the mass of the water to be added based on the air-dry mass of the material.

7.9 Weigh out this amount of water into a tared sprinkling jar.

7.10 Sprinkle water onto the soil during mixing, in increments.

7.11 Thoroughly mix each specimen to ensure even distribution of water throughout specimen.

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DENSITY RELATIONSHIP OF SUBGRADE, EMBANKMENT SOILS, AND TXDOT DESIGNATION: TEX-114-E
BACKFILL MATERIAL

7.12 Cover the mixed sample and allow sample to stand and cure for at least 12 hr. before
compacting. When the PI is less than 12, the curing time may be reduced to not less than
3 hr. Cure split or referee samples for the full 12 hr.

7.13 Assemble and secure the mold and collar to the base plate.

7.14 Thoroughly remix the cured sample.

7.15 Obtain approximately 1 lb. (453.6 g) of the sample and determine water content as
described in Tex-103-E, Section 7.

7.16 Place loose soil into the mold and spread into a layer of uniform thickness.

7.17 Before compaction, use hand tools to tamp the soil lightly until it is not fluffy or loose.

7.18 Separate the material in the pan into four equal portions. Each portion must contain
representative quantities of all sizes and adequate material to compact four 1.5-in.
(38-mm) layers.

7.19 For each layer, dump the material into the mold. Spade and level the layer of material
with a spatula to fill cavities around the edge and to ensure an even distribution of
material in each layer before compacting. Do not push this layer down by hand or other
means than that described above.

7.20 Compact each layer using 25 per lift with a drop height of 12 in. (304.88 mm).

7.21 Use the soil mass and compacted thickness of the first lift to adjust the mass and
thickness of the subsequent lifts.

7.22 Upon completion of compacting each of the first three lifts, use a knife or other
convenient tool to scarify the surface to a depth of 1/4 in. (6.3 mm). Dislodge
uncompacted soils that extend above the compacted surface.

7.23 Upon completion of the fourth lift, the compacted specimen should extend above the top,
but by no more than 1/4 in. (6.3 mm). Discard the compacted specimen if it does not
extend above the top of the mold at any point.

7.24 After compaction of the last lift, remove the collar and use a straight edge or draw knife
to carefully trim the compacted specimen even with the top of the mold.

7.25 Invert the mold and trim the bottom of the specimen even with the bottom of the mold.

7.26 Use trimmed soil from the specimen to fill holes on the trimmed surfaces. Trim again as
needed to ensure a smooth, level surface.

7.27 Determine and record the mass of the specimen and mold as WT to the nearest 0.001 lb.
(0.5 g) under Tex-113-E, Section 9.

7.28 Record the data on Form 1176, “M/D & Triaxial Worksheet.”

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DENSITY RELATIONSHIP OF SUBGRADE, EMBANKMENT SOILS, AND TXDOT DESIGNATION: TEX-114-E
BACKFILL MATERIAL

7.29 Use the hydraulic jack press to remove the specimen from the mold.

7.30 Place the compacted specimen and identification tag into a large pan and break into
several pieces.

7.31 Obtain the mass of the drying pan and wet sample and record to 0.001 lb. (0.5 g).

7.32 Place the specimen in an oven at a temperature of 230 ±9°F (110 ±5°C) and dry to
constant weight.
Note 3—Use a 140 ±9°F (60 ±5°C) oven for ML or MH soils (as determined by
Tex-145-E).

7.33 Record the mass of the oven-dried material to the nearest 0.001 lb. (0.5 g) under
Tex-113-E, Section 9.

7.34 Repeat Sections 7.8–7.33 for all samples.

8. CALCULATIONS

8.1 Use the equations in Tex-113-E, Section 9.

9. GRAPHS

9.1 Plot the molding moisture and dry density curve for Da as shown in Figure 1.

MOISTURE-DENSITY CURVE
96

94

92

90
DRY DENSITY (pcf)

88

86

84

82

80
20 22 24 26 28 30 32
MOISTURE CONTENT (%)

Figure 1—Plot of Sample Moisture-Density Curve

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DENSITY RELATIONSHIP OF SUBGRADE, EMBANKMENT SOILS, AND TXDOT DESIGNATION: TEX-114-E
BACKFILL MATERIAL

10. REPORTING TEST RESULTS

10.1 Report:
 Da to the nearest 0.1 lbs/ft3 (1 kg/m3)
 Wopt to the nearest 0.1 %.

PART II—MEASURING MOISTURE-DENSITY RELATIONSHIP OF

SUBGRADE AND EMBANKMENT SOILS

11. SCOPE

11.1 Part II uses a 6-in. (152.4-mm) diameter mold and applies only to soils with:
 100% passing the 7/8-in. (22.4-mm) sieve
 ≤ 20% passing the 1/4-in. (6.3-mm) sieve
 GM, GC, SM, or SC soil classifications as described by Tex-142-E

11.2 Use Tex-113-E for moisture-density curve determination of base materials and coarse-
grained materials containing particles larger than 7/8 in. (22.4 mm).

12. PREPARING SAMPLE

12.1 Secure a representative sample of material and prepare approximately 132 lb. (60 kg) of
moist soil as described in Tex-101-E, Part II for moisture-density test. Do not reuse soil
that has been previously laboratory compacted.

13. PROCEDURE

13.1 Determine the percent hygroscopic moisture of a representative sample of prepared

material in accordance with Tex-103-E.

13.2 Separate sample on 7/8-in. (22.4-mm), 3/8-in. (9.5 mm), and 1/4-in. (6.3 mm) sieves, and
determine the particle size distribution.

13.3 Estimate the mass of air-dried material that will fill the mold when wetted and
compacted.

13.4 Using this estimated mass and the percentages of the various sizes of particles obtained in
Section 13.2, compute the cumulative masses of each size to combine to make a
specimen.

13.5 Using the masses calculated in Section 13.3, recombine at least four specimens of
approximately 22 lb. (10 kg) each.

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DENSITY RELATIONSHIP OF SUBGRADE, EMBANKMENT SOILS, AND TXDOT DESIGNATION: TEX-114-E
BACKFILL MATERIAL

13.6 Estimate the optimum percent moisture required to attain maximum density.
Note 4—The plastic limit is a good indicator of optimum moisture content, typically
within 2%, or 3-4% higher for PI >35 material.

13.7 Start the M-D curve using a sample with a moisture content of 2% below the estimated
optimum moisture content. For soils with a low to moderate plasticity index (PI < 35),
adjust the moisture content of the remaining samples in approximately 2% increments to
attain two samples above and two samples below the optimum moisture content. For soils
with high plasticity index (PI ≥ 35), the moisture content may be adjusted in 4%
increments to attain two samples above and two samples below the optimum moisture.
Note 5—After compacting the first two or three specimens, the initial M-D curve can be
constructed to aid in evaluation of the shape of the curve. If necessary, adjust the water
content of the other prepared samples by adding additional water or air-drying to obtain a
well-defined compaction curve.

13.8 Calculate the mass of the water to be added based on the air-dry mass of the material.

13.9 Weigh the required mass of water into a tared sprinkling jar.

13.10 Sprinkle water onto the soil during mixing, in increments.

13.11 Thoroughly mix each specimen to ensure an even distribution of water.

13.12 Cover the mixed sample and allow sample to stand and cure for at least 12 hr. before
compacting. When the PI is less than 12, the curing time may be reduced to not less than
3 hr. Cure split or referee samples for the full 12 hr.

13.13 Assemble and secure the mold and collar to the base plate.

13.14 Thoroughly remix the cured sample.

13.15 Obtain approximately 1 lb. (453.6 kg) of the sample and determine water content as
described in Tex-103-E, Section 7.

13.16 Place loose soil into the mold and spread into a layer of uniform thickness.

13.17 Use hand tools to tamp the soil lightly until it is not fluffy or loose.

13.18 Separate the material in the pan into four equal portions. Each portion must contain
representative quantities of all sizes and adequate material to compact four 2-in. (50-mm)
layers.

13.19 For each layer, dump the material into the mold. Spade and level the layer of material
with a spatula to fill cavities around the edge and to ensure an even distribution of
material in each layer before compacting. Do not push this layer down by hand or other
means than that described above.

13.20 Compact each layer using 75 per lift with a drop height of 12 in. (304.88 mm).

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DENSITY RELATIONSHIP OF SUBGRADE, EMBANKMENT SOILS, AND TXDOT DESIGNATION: TEX-114-E
BACKFILL MATERIAL

13.21 Use the soil mass and compacted thickness of the first lift to adjust the mass and
thickness of the subsequent lifts.

13.22 Upon completion of compacting each of the first three lifts, use a knife or other
convenient tool to scarify the surface and dislodge the uncompacted soils that extend
above the compacted surface.

13.23 Use the finishing tools as outlined in Tex-113-E and four medium-firm blows of the 4 to
5 lb. (1.818 to 2.273 kg) rawhide hammer to level and finish the fourth lift.

13.24 Using the height-measuring stand, measure and record the specimen height to the nearest
0.001 in. (0.025 mm). The height of the finished specimen should be 8 ±1/4 in.
(2036.3 mm). Discard the specimen if it is too short or too tall.
Note 6—To adjust the molded height of specimen in Section 13.21, calculate as follows:

Dry Weight of Specimen = ( Dry Weight of Specimen × 8" ) / Height of Specimen

13.25 Determine and record the mass of the specimen and mold as WT to the nearest 0.001 lb.
(0.5 g), under Tex-113-E, Section 9.

13.26 Record the data on Form 1176, “M/D & Triaxial Worksheet.”

13.27 Use the hydraulic jack press to remove the specimen from the mold.

13.28 Place the compacted specimen and identification tag into a large pan and break into
several pieces.

13.29 Obtain the mass of the drying pan and wet sample and record to 0.001 lb. (0.5 g).

13.30 Place the specimen in an oven at a temperature of 230±9°F (110±5°C) and dry to
constant weight.
Note 7—Use a 140±9°F (60±5°C) oven for ML or MH soils (as determined by
Tex-142-E) or soils with measurable sulfates (as determined by Tex-145-E.)

13.31 Record the mass of the oven-dried material to the nearest 0.001 lb. (0.5 g) under
Tex-113-E, Section 9.

13.32 Repeat Sections 13.8–13.31 for all samples.

14. CALCULATIONS

14.1 Use the equations under Tex-113-E, Section 9.

15. GRAPHS

15.1 Plot the molding moisture vs. the dry density curve for Da shown in Figure 1.

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DENSITY RELATIONSHIP OF SUBGRADE, EMBANKMENT SOILS, AND TXDOT DESIGNATION: TEX-114-E
BACKFILL MATERIAL

16. REPORTING TEST RESULTS

16.1 Report test results as described in Part I.

PART III—MEASURING MOISTURE-DENSITY RELATIONSHIP OF

COHESIONLESS BACKFILL

17. SCOPE

17.1 Part III uses a 4-in. (102-mm) ID mold and applies only to cohesionless soils and
backfills as described below:
 100% passing the 1/4-in. (9.5-mm) sieve
 ≥ 50% passing the No. 4 (4.75-mm) sieve
 ≤ 25% passing the No. 200 (75-mm) sieve
 SW – SP classification.

18. PREPARING SAMPLES

18.1 Prepare the material in accordance with Tex-101-E, Part II.

19. PROCEDURE

19.1 Perform Part I, Sections 7.1–7.15, except for Section 7.12.

19.2 Mix the material thoroughly and separate into four equal portions. Each portion must
contain representative quantities of all sizes and contain enough material to compact four
1.5-in. (38-mm) layers.

19.3 For each layer, dump the material into the mold. Spade and level the layer of material
with a spatula to fill cavities around the edge and to ensure an even distribution of
material in each layer before compacting. Do not push this layer down by hand or other
means than that described above.

19.4 Compact each layer by applying 61 ram blows with a 10-lb. (4.55-kg.) rammer from a
height of 12 in. (457.2 mm).

19.5 Stop the compactor as frequently as necessary to clean the ram face.

19.6 Use the soil mass and compacted thickness of the first layer to adjust the mass and
thickness of the subsequent layers.

19.7 Each layer thickness should be approximately equal in height and mass. All material
should be molded.

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DENSITY RELATIONSHIP OF SUBGRADE, EMBANKMENT SOILS, AND TXDOT DESIGNATION: TEX-114-E
BACKFILL MATERIAL

19.8 Upon completion of the fourth lift, the compacted specimen should extend above the top,
but by no more than 1/4 in. (6.3 mm). Discard the compacted specimen if it does not
extend above the top of the mold at any point.

19.9 Remove the collar and use a straight edge or draw knife to carefully trim the compacted
specimen even with the top of the mold.

19.10 Use trimmed material from the specimen to fill holes on the trimmed surfaces. Trim
again, as needed to ensure a smooth, level surface.

19.11 Determine and record the mass of the specimen and mold as WT to the nearest 0.001 lb.
(0.5 g) under Tex-113-E, Section 9.

19.12 Record the data on Form 1176, “M/D & Triaxial Worksheet.”

19.13 Carefully center the specimen over a porous stone and place in the hydraulic press to
extrude the specimen from the mold.

19.14 Place the compacted specimen and identification tag into a large pan and break into
several pieces.

19.15 Obtain the mass of the drying pan and wet sample and record to 0.001 lb. (0.5 g).

19.16 Place the drying pan with wet material in an oven at a temperature of 230°F (110°C) and
dry to constant weight.

19.17 Record the mass of the oven-dried material to the nearest 0.001 lb. (0.5 g) under
Tex-113-E, Section 9.

19.18 Repeat Sections 19.2–19.17 for all samples.

Note 8—After compacting the first two or three specimens, the initial M-D curve can be
constructed to aid in evaluation of the shape of the curve. If necessary, adjust the water
content of the other prepared samples by adding additional water or air-drying to obtain a
well-defined compaction curve.

20. CALCULATIONS

20.1 Use the equations under Tex-113-E, Section 9.

21. REPORTING TEST RESULTS

21.1 Report test results as described in Part I.

22. FAMILY OF CURVES

22.1 The materials used for subgrade and embankment construction are variable in color,
texture, and moisture-density relationship.

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DENSITY RELATIONSHIP OF SUBGRADE, EMBANKMENT SOILS, AND TXDOT DESIGNATION: TEX-114-E
BACKFILL MATERIAL

22.2 To adequately control the compaction and field densities of these materials, it is
necessary to have several compaction curves prepared and plotted on the same graph to
assist the inspector to make a sound judgment as to which curve is representative of the
material being tested for field density.

22.3 The family of compaction curves shown in Figure 2 illustrates that, as the material's
plasticity and fineness increase, the Da will decrease with a corresponding increase in
Wopt. Also the wet leg of the compaction curve generally parallel with the 0% air void
line.

22.4 To properly correlate the soil properties to a compaction curve, the soil properties
presented in Table 1 should be provided along with the family of compaction curves.

Table 1—Soil Properties, Family of Curves, & One-Point Control

Curve Max. Dry Optimum Liquid PI Wet Gradation, % Retained Material

No. Density kg/m3 Water Limit Description
(pcf) Content % %

22.4 mm 9.5 mm 4.75 mm

(7/8 in.) (3/8 in.) (No.4)

1 93.6 (1499.5) 22.0 61 43 0 0 0 dark brown clay

2 96.6 (1547.5) 20.4 48 30 0 0 1.4 brown clay
3 100.3 (1606.8) 18.8 44 27 0 0 2.5 brown clay
4 104.6 (1675.7) 17.4 38 21 0 0 4.3 lt. brown clay

23. ONE-POINT CONTROL

23.1 In the event the material being tested for field density does not match the description and
properties of any of the materials from the family of compaction curves, the one-point
control method may be used to derive an adjusted Da and Wopt by:
 air drying the field sample to a water content near the plastic limit of the material
 molding one compaction specimen
 using the one-point moisture-density data to construct a compaction curve which
mimics the shape of the family of curves

23.2 The wet leg of the compaction curve is well defined by the 0% air void line; therefore, it
is essential to air-dry the field sample to a water content near the plastic limit of the
material and provide better definition of the dry side of the curve. An example of the one-
point control method is shown on Figure 2.

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BACKFILL MATERIAL

110

108

106

104

102

100
DRY DENSITY, pcf

One Point
Moisture-Density
98

96

94

92

90

88

86
10 12 14 16 18 20 22 24 26 28 30
MOISTURE CONTENT, %

FAMILY OF CURVES & ONE POINT CONTROL (EXAMPLE)

Figure 2—Family of Curves & one-Point Control (Example).

24. ARCHIVED VERSIONS

24.1 Archived versions are available.

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